So, we must reduce hardships of single mothers. That of course means certain cost to the society, but thanks to that, children of single mothers would be productive members of society. This will make it easier to be a single mother. Thanks to that, woman would be more willing to be single mothers. That would increase costs to the society.

Of course, there are two more factors: one, that some research seems to indicate that males raised by single mothers tend to be impacted much worse than females; second, that there might be that single mothers are single because they have inherited certain traits making them mor esusceptible to being single mothers (amongst other things), and making easier for them to have children will simply increase the number of their children, making more children with such traits (like low impulse control etc).